box/hookeslaw.hh

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#ifndef DUMUX_DISCRETIZATION_BOX_HOOKES_LAW_HH
#define DUMUX_DISCRETIZATION_BOX_HOOKES_LAW_HH
 
#include <dune/common/fmatrix.hh>
 
#include <dumux/flux/hookeslaw.hh>
#include <dumux/discretization/method.hh>
#include <dumux/discretization/extrusion.hh>
 
namespace Dumux {

template<class ScalarType, class GridGeometry>
class HookesLaw<ScalarType, GridGeometry, DiscretizationMethod::box>
{
    using FVElementGeometry = typename GridGeometry::LocalView;
    using SubControlVolumeFace = typename GridGeometry::SubControlVolumeFace;
    using Extrusion = Extrusion_t<GridGeometry>;
 
    using GridView = typename GridGeometry::GridView;
    using Element = typename GridView::template Codim<0>::Entity;
 
    static constexpr int dim = GridView::dimension;
    static constexpr int dimWorld = GridView::dimensionworld;
    static_assert(dim == dimWorld, "Hookes Law not implemented for network/surface grids");
 
public:
    using Scalar = ScalarType;
    using StressTensor = Dune::FieldMatrix<Scalar, dim, dimWorld>;
    using ForceVector = typename StressTensor::row_type;
    static constexpr DiscretizationMethod discMethod = DiscretizationMethod::box;

    template<class Problem, class ElementVolumeVariables, class ElementFluxVarsCache>
    static ForceVector force(const Problem& problem,
                             const Element& element,
                             const FVElementGeometry& fvGeometry,
                             const ElementVolumeVariables& elemVolVars,
                             const SubControlVolumeFace& scvf,
                             const ElementFluxVarsCache& elemFluxVarCache)
    {
        const auto sigma = stressTensor(problem, element, fvGeometry, elemVolVars, elemFluxVarCache[scvf]);
 
        ForceVector scvfForce(0.0);
        sigma.mv(scvf.unitOuterNormal(), scvfForce);
        scvfForce *= Extrusion::area(scvf);
 
        return scvfForce;
    }

    template<class Problem, class ElementVolumeVariables, class FluxVarsCache>
    static StressTensor stressTensor(const Problem& problem,
                                     const Element& element,
                                     const FVElementGeometry& fvGeometry,
                                     const ElementVolumeVariables& elemVolVars,
                                     const FluxVarsCache& fluxVarCache)
    {
        const auto& lameParams = problem.spatialParams().lameParams(element, fvGeometry, elemVolVars, fluxVarCache);
 
        // evaluate displacement gradient
        StressTensor gradU(0.0);
        for (int dir = 0; dir < dim; ++dir)
            for (const auto& scv : scvs(fvGeometry))
                gradU[dir].axpy(elemVolVars[scv.indexInElement()].displacement(dir), fluxVarCache.gradN(scv.indexInElement()));
 
        // evaluate strain tensor
        StressTensor epsilon;
        for (int i = 0; i < dim; ++i)
            for (int j = 0; j < dimWorld; ++j)
                epsilon[i][j] = 0.5*(gradU[i][j] + gradU[j][i]);
 
        // calculate sigma
        StressTensor sigma(0.0);
        const auto traceEpsilon = trace(epsilon);
        for (int i = 0; i < dim; ++i)
        {
            sigma[i][i] = lameParams.lambda()*traceEpsilon;
            for (int j = 0; j < dimWorld; ++j)
                sigma[i][j] += 2.0*lameParams.mu()*epsilon[i][j];
        }
 
        return sigma;
    }
};
 
} // end namespace Dumux
 
#endif